US 6485423 B2 Abstract A method of correcting for phasefront aberrations in ultrasound imaging uses highly spaced apart point scatterers artificially placed in the tissue being imaged. The point scatterers reflect the transmitted sound and are individually differentiated to provide singular reference points for correction of signals reflected from the surrounding tissue. The differentiation is performed by comparison of the third or fourth harmonic frequencies of the reflected signals. To ensure the necessary high dispersal of the point scatterers, high amplitude pulses of the transmitted signal destroy point scatterers in selected image regions. In an alternate embodiment, correction is performed by stochastic analysis of signals reflected from the highly dispersed point scatterers. A reference signal is compared to the second harmonic of the reflected signal to reduce noise.
Claims(43) 1. A method for corrections of phasefront aberrations and pulse reverberations in medical ultrasound imaging, where
ultrasound beams on transmit and/or receive are formed with an ultrasound transducer array that has a two-dimensional distribution of elements, a maximal linear dimension of the elements being smaller than a spatial correlation length of the phase amplitude seen across the array surface,
a individual array element signals are filtered in a correction filter before standard beam forming is done, both for the transmit and/or the receive beams,
the correction filters are estimated by
introducing into a soft tissue image field one or more artificial ultrasound point scatterers,
receiving backscatterd signal from the point scatterers with the transducer array,
the point scatterers being spaced apart that the signals from the individual scatterers can clearly be discriminated from each other,
the signals from the point scatterers having characteristics in amplitude or frequency content, or both, so that they are clearly separable from the tissue signal,
the signals from the individual point scatterers being used to derive correction filters to correct for phase aberrations and pulse reverberations both in the receive and the transmit beams.
2. A method according to
Fourier transforming along time coordinate the received element signals from the point scatterers and utilizing the frequency components where amplitude of the Fourier transform is larger than the noise level,
correcting phase of the Fourier transforms of the element signals by a spherical approximation of a propagation delay from the point scatterer to the array elements, which is in essence a division of the Fourier transform with the Green's function of the Helmholtz equation,
the complex conjugate of the corrected Fourier transforms of the elements signals being used as transfer functions of element signal correction filters for the receive and/or the transmit beams.
3. A method according to
recording the back scattered element signals from the point scatterer and delay correcting these element signals by a spherical approximation of propagation delay from the point scatterer to the individual array elements,
using time inverted version of the delay corrected element signals as impulse responses for the element signal correction filters for the receive and/or the transmit beams.
4. A method according to
5. A method according to
the amplitude corrections for each element signal are obtained as the amplitude of the received element point scatterer signals, and
the time delay corrections are obtained by comparing arrival times on each element signal channel of the pulses from the point scatterer.
6. A method according to
^{nd }harmonic band of the backscattered element signals are used to reduce the pulse reverberations in the backscattered signal for estimation of the correction filters or approximate amplitude and delay corrections.7. A method according to
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^{nd}, 3^{rd}, or 4^{th }harmonic band of the fundamental frequency band of the transmitted pulse.14. A method according to
15. A method for corrections of phasefront aberrations and pulse reverberations in medical ultrasound imaging, where
the ultrasound beams on transmit and/or receive are formed with an ultrasound transducer array that has a two-dimensional distribution of elements, a maximal linear dimension of the elements being smaller than a spatial correlation length of the phase amplitude seen across the array surface,
individual array element signals being filtered in correction filters before standard beam forming is done, both for the transmit and/or the receive beams,
the correction filters being estimated from the received element signals from the array elements back scattered from a distribution of scatterers with short correlation length,
using an estimation algorithm for the correction filters that reduces the effect of pulse reverberations in the backscattered signal in a final estimate of correction filters.
16. A method according to
^{nd }harmonic band of the element signals is used to suppress the pulse reverberations in the element signals.17. A method according to
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^{nd}, 3^{rd}, or 4^{th }harmonic components of the backscattered signal from the contrast agent bubbles.22. A method according to
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Description This application claims priority from Provisional application Ser. No. 60/179,196, filed Jan. 31, 2000. 1. Field of the Invention The present invention is directed to methods for estimating corrections for the image degradation produced in medical ultrasound images by phasefront aberrations and reverberations. The method hence has applications to all situations were ultrasound imaging is used in medicine, and also other similar situations of ultrasound imaging. 2. Description of the Related Art With ultrasound imaging of objects through complex structures of tissue, the following effects will degrade the images i) Variations of the acoustic velocity within the complex tissue structures produce aberrations of the acoustic wavefront, destroying the focusing of the beam mainlobe and increasing the beam sidelobes.* ii) Interfaces between materials with large differences in acoustic properties can give so strong reflections of the ultrasound pulse that multiple reflections get large amplitudes. Such multiple reflections are termed pulse reverberations, and add a tail to the propagating ultrasound pulse, which shows as noise in the ultrasound image.* The reduced focusing of the beam main lobe reduces the spatial resolution in the ultrasound imaging system. The increase in beam side lobes and the pulse reverberations, introduce additive noise in the image, which is termed acoustic noise as it is produced by the transmitted ultrasound pulse itself. Increasing the transmitted pulse power will hence not improve the power ratio of the signal to the noise of this type, contrary to what is found with electronic receiver noise. The materials with largest differences in acoustic properties are muscles, fat, connective tissue, cartilage, bone, air, and the ultrasound transducer itself. Mixtures of fat, muscles, connective tissue and cartilage in the body wall can therefore produce very large phase front aberrations and reverberations. Especially, one will get strong reverberations from the transducer reflections of the returning signals from interfaces of such tissues in the body wall. The mixtures of such tissues in the body wall are therefore the major cause of the degradation found with non-invasive ultrasound imaging in many patients. Reducing the effect of the reverberations and phase front aberrations in the body wall is hence much needed in many applications of medical ultrasound imaging. With a two-dimensional transducer array, the effect of the phasefront aberrations can in many situations be reduced by adding corrective delays and gain factors to the signals for the individual array elements, in the following referred to as element signals. This has been presented in many papers. In more complex situations of tissue mixtures, the phasefront aberrations and pulse reverberations can produce modifications of the pulse form. It is less known that such pulse modifications can be corrected by a filter for each of the element signals. Such correction filters gives the most general correction method, and delay/amplitude corrections can be considered as a special case or an approximation of correction filters. 2 Transmitting a pulse with center frequency around f The 2 i) The 2 ii) As the transmitted frequency f However, when the back-scattered signal passes the body wall on its return, the 2 Although the principle of correction for phasefront aberrations and pulse reverberations is well defined, it is in the imaging situation generally difficult to determine the correction filters or the simplified delay and amplitude corrections. The present invention devices two solutions to this problem: i) The backscattered signal from point scatterers that are artificially introduced into the body serves as beacons to determine the correction filters. Such point scatterers are either connected to intervention tools that are introduced into the body, for example a biopsy needle, or ultrasound contrast agent bubbles in such a dilute concentration that the signals from individual bubbles can be discriminated from each other. The point scatterers must be so spaced apart that the signals from different point scatterers are clearly differentiable from each other and be so strong that they are differentiable from the tissue signal. To maintain adequate distance between the bubbles, the invention devices to use high transmitted pulse amplitudes to destroy the bubbles in selected image regions, so that for an adequate interval of time after this bubble destruction, new inflow bubbles have adequate distance to each other. Consecutive transmission of high amplitude pulses into the region can be used for repeated destruction of the bubbles so that a continuously changing set of point scatterer bubbles in the image region is obtained. To discriminate the bubble signal from tissue signal one can typically use backscattered frequency components in a band around the the 3 ii) With the other method one uses stochastic analysis of the back-scattered signal from distributed scatterers with short correlation length compared to the wave length. One general problem for such analysis is that the backscattered signal is corroborated with acoustic noise from pulse reverberations and phase front aberrations, and the invention devices two methods for reduction of such acoustic noise before the determination of the correction filters: a) The 2 b) The body wall pulse reverberations are fairly stationary in time. By using the backscattered signal from moving or time varying scatterers obtained with multiple transmit pulses with the same focus and beam direction, the temporally stationary acoustic noise is suppressed by highpass filtering each range in the backscattered signal along the pulse number coordinate, so that mainly the signals from the moving scatterers passes the filter for further processing. Typical moving scatterers can be the myocardium or an arterial wall, or scatterers found in blood or other body fluids. To enhance the scattering from such fluids, the invention also devices the use of ultrasound contrast agent to be injected into the body fluid. Time varying scatterers can be ultrasound contrast agent where so high transmit pulses are used that one get destruction of at least some of the contrast agent bubbles between the pulses.* The stochastic analysis commonly contains an averaging of signal parameters, where averaging of signal parameters from different depths or possibly also different beam directions typically can be used. Such methods often provides a limited number of samples to average, which gives variance noise in the estimates. To improve the estimation robustness and reduce the variance in the estimates, the invention devices a method that uses the backscattered signal from moving or time varying scatterers acquired with multiple transmit pulses with the same focus and beam direction. Signal parameters obtained for each transmit pulse are then averaged for many transmit pulses, possibly in combination with averaging over depth and beam direction, to reduce the variance in the estimates. In addition to these basic principles, the invention devices several detailed methods for estimation of the correction filters. Strong scatterers off the beam axis, can introduce interference in the correction estimates, and the invention devices methods to reduce the effect of such scatterers, using spatial lowpass filtering of the received signal across the transducer surface, or highpass filtering of estimated correction phases or delays across the transducer surface. Such highpass filtering can conveniently be done by expanding the correction delays in a generalized Fourier series, for example using Legendre polynomials as basis functions, and leaving out the lowest coefficients that relates to offset direction and possible offset focusing of the scatterer. The correlation length of the phase aberrations and pulse reverberations along the transducer array surface has a lower bound. One can therefore also truncate the generalized Fourier series at the upper end, reducing the total number of coefficients in the series. The information carrying coefficients in the generalized Fourier series is hence a reduced parameter set that represents the correction filters, and is conveniently estimated in a parameter estimation scheme. Often one also find that the correlation length of the phase aberrations and pulse reverberations along the transducer array surface is larger than the array element dimensions, as for example with phased arrays for sector steering of the beam. For this situation the invention devices combination of the element signals from neighboring elements before estimation of the correction filters. This combination reduces the total number of signal channels used in the estimation, hence simplifying the processing and increasing the signal to noise ratio in the resulting channel. Other objects and features of the present invention will become apparent from the following detailed description considered in conjunction with the accompanying drawings. It is to be understood, however, that the drawings are designed solely for purposes of illustration and not as a definition of the limits of the invention, for which reference should be made to the appended claims. It should be further understood that the drawings are not necessarily drawn to scale and that, unless otherwise indicated, they are merely intended to conceptually illustrate the structures and procedures described herein. In the drawings: FIG. 1 shows a typical measurement situation where the ultrasound array in contact with the skin transmits ultrasound pulses through the body wall, which is a mixture of fat, muscles, and connective tissue. The outbound pulse is modified by phase aberrations and pulse reverberations as it passes the body wall. A point scatterer, scatters a spherical wave which is modified by reverberations and phase front aberrations as it returns through the body wall. FIG. 2 shows an example of a practical focal plane beam profile that is obtained for a phase aberrated pulse together with a corrected beam profile and the ideal beamprofile obtained without phase aberrations. FIG. 3 In a) shows the use of artificially introduced point scatterers on an intervention tool for estimation of correction filters. In b) is shown an example block diagram of a unit for estimation of correction filters both from point scatterers and distributed scatterers, and how the correction filters are used for corrections of phase aberrations and pulse reverberations both in the receiver and the transmit beams. FIG. 4 shows in a) a block diagram of a FIR filter for corrections of element signal no. n in the receiver beam former, while in b) is shown a unit for correction of transmitted signal on element no. n in the transmit beam former. FIG. 5 shows the use of artificially introduced point scatterers in the form of contrast agent bubbles that are introduced at low concentration in the blood or other body fluids. FIG. 6 shows the coordinate system used for calculating the expressions of the element signals. FIG. 7 shows in a) the prism type refraction effect of the ultrasound beam produced by a wedge shaped fat layer in the body wall, and in b) the added effect of miss-estimating the location of the center of gravity of the scatterer distribution by a strong scatterer in the beam side lobe. FIG. 8 shows a method of hierarchical integration of the neighbor difference in the phase or delay correlations, to reduce the effect of drift in the integration process produced by estimation errors. FIG. 1 shows a typical measurement situation where an ultrasound transducer array ( At reflection of the pulse from a point scatterer ( In order to focus the receiver beam onto the point scatterer, a standard receiver beam former will delay the individual array signals a time interval calculated from the assumption that the wavefront that arrives from the point scatterer has a spherical shape. Amplitude apodization of the array element signals is also used to reduce the sidelobes in the focal plane. When the real phase front ( In the linear approximation of wave propagation in the tissue, all aspects of the propagation is contained in the Green's function. This function gives the wave-field from a unit point source located at all source points
_{f};ω)=s( r,r _{f};ω)g _{h}( r−r _{f};ω) (1)where c is the wave propagation velocity in the homogeneous tissue. s( When there is no power absorption in the tissue, it has been shown by M. Fink [1], that time-reversal of the received element signals from a point source in a two-dimensional array, produces the optimal correction of the element transmit signals, for focusing the transmit beam onto the point source. This is equivalent to setting up the transmit beam former in the standard way assuming homogeneous tissue with constant wave velocity, and then filtering the transmit pulses at the element location
_{f};ω)=s*( r,r _{f};ω) (3)where * denotes complex conjugation. By reciprocity of the transmit and the receive beams, we also get optimal focusing of the receive beam onto the point target at The reason one must use a two-dimensional array for corrections of the body wall disturbances is that the body wall produces a two-dimensional disturbance pattern over the transducer array. The correlation length of the disturbances has however a lower limit, so that the width of the elements used in the correction can be larger than typical element widths in many electronic arrays, for example the phased array. For efficient processing, one can in such situations combine the element signals from neighboring, narrow elements to give fewer element signals from larger elements, that are still smaller than the correlation length of the disturbances over the array. With uniform acoustic power absorption in the tissue, the gain and phase variations of s* will still correct for the spatial variations in propagation velocity in the tissue and hence reduce the effect of phase aberrations and pulse reverberations. The absorption will, however, attenuate the pulse and also produce some pulse stretching since the power absorption increases with frequency. These effects can be compensated for by a depth variable gain and filter. Strongly heterogeneous absorption will produce spatial amplitude variations in the Green's function that requires special compensation not accounted for by H From the definition in Eq.(1) we see that one can determine s( In a first aspect, the invention devices the introduction of artificial point scatterers with signal that is clearly differentiable in amplitude or frequency content from the tissue signal, so that g( According to the invention, the point scatterers can be introduced on an intervention tool, like a biopsy needle, for improved imaging of the tissue around the needle, especially the biopsy target around the needle tip and also to avoid critical areas around the needle tip when it is introduced, like blood vessels. An example of such a situation is shown in FIGS. 3 The correction estimation unit The received ultrasound RF-lines As the first point scatterer Corrections of the receive element signals could typically be done in a filter unit shown for one single element signal no n as The output According to the invention, the point scatterers can also be introduced as a dilute concentration of contrast agent bubbles, so that the bubbles in the tissue are so spaced apart that their signals can be discriminated from each other, as illustrated in FIG. Each contrast bubble reflects when they are hit by an incident ultrasound pulse, a set of non-linearly distorted pulses that propagates as spherical waves, where one in the example illustrates the wave To discriminate contrast bubble signal from the surrounding tissue signal, one can use the sub, 2 To avoid unwanted destruction of the contrast agent bubbles, the incident pulse amplitude in the tissue must be kept limited. Maintaining this limit in the incident pulse, one can improve the signal to noise ratio in the received element signals by transmission of coded pulse sequences with subsequent pulse compression in the receiver, and hence reduce the noise in the estimated s( Such contrast bubbles are also good candidates for point scatterers to be attached at localized sites on intervention tools. In the second aspect of the invention, the present patent devices a method for estimating s( A presupposition is that the scatterers used to estimate s(
_{1})ν( r _{2})>=σ_{ν} ^{2}( r _{1})δ( r _{2} − r _{1}) (4)< > denotes ensemble averaging over a mathematically defined outcome ensemble to be further discussed below, and σ The outcome ensemble is a selected set of scattering distribution functions, where the particular scatterer distribution found in an experiment is considered an outcome or realization of the ensemble. As one in the experimental situation can not observe all outcomes of the ensemble, it is with practical experiments generally a problem to carry through an ensemble averaging as defined above. For spatially stationary scatterer distributions, one can to a limited degree substitute ensemble averaging with spatial averaging over the regions of scatterer positions The present invention also devices an additional method for estimating ensemble averaging of signal parameters, where one uses the signal from moving scatterers observed with consecutive transmit pulses with the same focus and amplitude, separated with so large intervals in time that the scatterers are exchanged in the actual region for each transmit pulse. Hence, the signal from each transmit pulse can be considered as an outcome of the ensemble, and averaging of signal parameters for a particular region can be done by averaging over the signal from the consecutive transmit pulses, which is further described below. To obtain time varying scatterers in a tissue region that otherwise has limited movement, and where adequately large blood vessels where the blood can be used as moving scatterers, are missing, one can insert ultrasound contrast agent into the blood vessels, which subsequently flows into the capillaries of the tissue region. With a high amplitude of the incident imaging pulses, some or all of the contrast agent bubbles within the beam can be destroyed. This destruction combined with the new inflow of contrast agent bubbles to the tissue region can be used to produce variation of the contrast agent bubbles in the imaging region between pulses. Temporal averaging of signal parameters of the backscattered signal from the contrast agent for a set of transmitted pulses, can then be used as an estimate of ensemble averages. Using the expression for the Green's function in Eq.(1), we get the following expression for the spatial frequency response of the transmitted beam at where S The coordinates are illustrated in FIG. 6, where the transducer surface S Around the focus where In the focal surface S The focal beam profile H
_{1} , r _{f};ω)≈e ^{−ikr} ^{ 1 } F(r _{1} −r _{f})H _{et}( r _{1} , r _{f};ω) (9)which will be used in the following analysis. The temporal Fourier transform of the received signal at location where P(ω) is the temporal Fourier transform of the received pulse from a point scatterer, and σ( σ( _{1};ω)=−k ^{2} H _{t}( r _{1} , r _{f};ω)ν( r _{1}) (11)We note from Eqs.(4, 11) that σ is δ-correlated in space, i.e.
_{1};ω)σ( r _{2};ω)>=σ^{2} _{σ}( r _{1};ω)δ( r _{2} − r _{1}) σ^{2} _{σ}( r _{1};ω)=k ^{4} |H _{t}( r _{1} , r _{f};ω)|^{2}σ^{2} _{ν} (12)For steering and focusing the receive beam onto
y( ;ω)2r πr _{f} e ^{−iωτ} ^{ sf } ^{(r,r } ^{ f } ^{)} ωτ_{sf}( r,r _{f})=kr _{f} −k| r−r _{f}| (13)where τ We shall now analyze a situation where the phase-amplitude screen varies so slowly with the scatterer position As σ is a δ-correlated process with zero mean, y where the averaging is done over an infinite number of different outcomes of the scatterer distribution, i.e. ensemble averaging. From Eq.(14) we note that we can use the following approximation Inserting the approximation of H We note that the two-dimensional, lateral part of the integral is the inverse Fourier transform of |H where A is a constant. Especially we note that for zero lag we have and utilizing Eq.(18) we get To find the amplitude-phase screen we express it by its amplitude a _{f};ω)=a _{s}( r,r _{f};ω)e ^{iθ} ^{ s } ^{(r,r } ^{ f } ^{;ω)} (21)The amplitude of the screen is obtained from Eq.(15) with zero space displacement We note that R Solving for the integral of |s| which inserted into Eq.(22) gives We note that for Gaussian variables we have This gives the following modified estimation of the screen amplitude in Eq.(25) To find the phase of the screen, we note that We utilize the spatial gradient of the auto-correlation function as ∇ s*( r,r _{f};ω)∇_{ξ} s( r+ξ,r _{f};ω)R _{f}( r,ξ;ω)
_{f};ω)s( r+ξ,r _{f};ω)∇_{ξ} R _{f}( (29)r,ξ;ω)Noting that ∇
;ω)=0 s*( r,r _{f};ω)∇_{r} s( r,r _{f};ω)R _{f}( r,0;ω)+
_{f}; ω)|^{2}∇_{ξ} R _{f}( r,0;ω) (30)which allows us to calculate We express the auto-correlation function by its amplitude and phase as
A _{R}( )r,ξ;ωe ^{iθ} ^{ R } ^{(r,ξ;ω) } a) R _{f}( )=r,ξ;ωA _{Rf}( )r,ξ;ωe ^{iθ} ^{ Rf } ^{(r,ξ;ω) } b) (32)In analogy with Eq.(28) we get Comparing with Eq. (31) we hence get ∇ _{f};ω)=∇_{ξ}θ_{R}( r,0;ω)−∇_{ξ}θ_{Rf}( r,0;ω) (34)Integrating this expression with respect to From Eqs.(15, 33) we hence get where θ ∇ _{1};ω)≈k( e _{r1−r} − e _{rf−r} (37)where where we in the last expression have substituted Eq.(12) with constant σ The above expression can be written in the short form as where ∇ _{f};ω)=∇_{ξ}θ_{R}( r,0;ω)−k( e _{rc−r} − e _{rf−r} (40)This equation can be integrated as We note that the term −k(| With a homogeneous scatterer distribution the center of gravity of σ Hence, deviation of where We notice that the integration over Inserting ∇s from Eq.(28) gives The numerator of the last term can be expanded by Gauss theorem as where the last integral is taken along the boundary of S Inserting Eq.(40) we see that We do not in general know
_{f};ω)=∇_{ξ}{circumflex over (θ)}_{R}( r, (49)0;ω)where the hat for θ This phase estimate will not correct for refraction and focusing offset due to a plane/spherical component with Any DC-offset of ∇θ and then modify the estimate by subtracting a plane component as
_{f};ω)=θ_{s}( r,r _{f};ω)−k _{1} x _{1} −k _{2} x _{2} (52)where k which gives This method would also be useful where θ The uncorrected transmit beam will have increased width of the mainlobe and high sidelobes. The approximation in Eq.(14a) that s( One hence can use an iterative scheme where a first estimate of the phase-amplitude screen, s( As stated in relation to Eq.(4), the ensemble averaging above presents practical problems with measurements, where we for a defined image of the tissue are observing a single outcome of the scattering distribution. A first approximation is to substitute ensemble averaging of signal parameters with spatial averaging over several depths along a fixed beam direction, with possible additional averaging of the signal parameters over neighboring beam directions. There are two problems with this averaging method: i) Reverberations between structures inside the body wall, and between these structures and the transducer, will produce additive reverberation noise n y _{f}( )+r;ωn _{f}( ) (55)r;ωThis noise will corroborate the estimates of the correlation functions for y ii) Variations of the phase aberrations and reverberations with scatterer position limits the size of the averaging region which leaves fundamental variance noise in the estimates of the correlation functions.* For the problem i) we note that 2 Let {z which gives an estimate of the received signal as
z _{fk}( r;ω)−{circumflex over (n)} _{f}( ω) (57)r;Such filtering will also remove the signal from stationary scatterers within V
H _{HP,k}(z _{fk}( )) (58)r;ωV H _{LP,r } {H _{HP,k}(z _{fk}( )) (59)r;ωThe bandwidth of this lowpass filter is the same as the bandwidth of y For problem ii) the present patent presents a method to reduce the estimate variances by utilizing the signal from moving or time varying scatterers. The basis for this is that the body wall aberrations and reverberations are comparably stationary in time, so that one can use many transmit pulses for the estimates of the correction filters. With sufficient time lag between consecutive transmit pulses, convection or time variation of the scatterers changes the scatterers in the actual region between transmit pulses. Additional averaging in the statistical analysis can then be done over the received element signals from many transmit pulses with different scatterers. This allows one too choose a spatial range of the signal used in the estimation that is small, minimizing the variation of s( With signal processing in the temporal domain, as described below, one can even use signal ranges down to a fixed, single depth sample for the calculation of the statistical parameters of the element signals. This only requires that the phase aberrations and reverberations are practically independent of scatterer position over the range cell, which is determined laterally by the width of the transmitted beam, and radially by the length of the transmitted pulse. This method hence sets the minimal requirement for invariance of the phase aberrations and reverberations with scatterer position. As the correlation estimates must be done by averaging over a limited spatial region and a limited number K of transmit pulse measurements, we will have errors in the correlation estimates. These errors will have a correlation length in the displacement coordinate FIG. 8 shows a block diagram of a hierarchical method to integrate the ∇θ As the phase gradient is integrated only over a limited number of neighboring elements, the integration drift is kept at a minimum. Other methods to estimate the phase screen are also useful, and we shall here present a method using the maximum likelihood in the Fourier domain, and a method using a reference signal for the correlation For the maximum likelihood method we let m and n label the element signals used for the correction estimation. We assume that possible combination of signals from neighboring elements which are small compared to the correlation length of the body wall disturbances across the array, can be done prior to the estimation, so that the element signals used for the estimation can be different from the array element signals. k labels the signal segments used for averaging, which can be selected as depth ranges for each transmit pulse over several transmit pulses for the same beam direction. Addition of signals from several neighboring beam directions can also possibly be done. We then define a measurement vectors
_{k} ={y _{kn} }={y _{fk}( r _{n};ω)}={s( r _{n} , r _{f};ω)f _{k}( r _{n} , r _{f};ω)}= f _{k}S k=1, . . . , K where we in the vector and matrix notations have omitted ω for simplicity, defining _{k} ={f _{kn} }={f _{k}( r _{n} , r _{f};ω)} S={S _{mn} }={s( r _{n} , r _{f};ω)δ_{mn} (60)We also use the compact notation
_{K} ={ y _{k} ,k=1, . . . , K The conditional probability of obtaining the measurement where we have defined
_{k}
y
_{1}
>=Yδ
_{kl }
Y={Y
_{mn}
}={<y*
_{km}
y
_{kn}
>}=S*<
f*_{k}
f
_{k}
>S=S*FS
_{k} f _{1} =Fδ _{kl } F={F _{mn} }={<f* _{km} f _{kn}>}We now determine the S that maximizes the p( with respect to a Differentiating L with respect to θ where R The expression in the brackets hence must be real, which requires that This is a non-linear equation, which can be solved with several numerical iteration schemes, for example as where q labels the iteration step. A starting value for the iteration can be θ A reference signal can for example be obtained as the full sum of all the receive element signals, referred to as the beam sum reference, or as a sum of subgroups of the receive element signals, referred to as a subgroup reference. The subgroup reference is for example useful with hierarchical methods as described in FIG. 8, where each subgroup can use a subgroup reference formed as the sum of the signals in the subgroup. An advantage with the use of the reference signal is that the screen amplitude and phase can for each receiver channel be determined by correlation between the element signal for this channel and the reference signal, hence avoiding the integration in Eq.(50) with its drift problems. A reference signal of the type described, can then be expressed as where the label k indicates transmit pulse number and S The correlation between the reference signal and an element signal is then where the label k is omitted since we are calculating ensemble averages. Inserting the δ-correlation of σ from Eq.(12) then gives Inserting the expression for R Comparing with Eq.(8) we see that the last integral in Eq.(71) represents the complex conjugate of the focal beam profile of a transducer composed of the elements of S Inserting Eqs.(12, 9), we get We note that the integral has the form of an inverse Fourier transform in relation to Eq.(8), and further evaluation gives We hence see that the phase of the reference signal correlation is the phase of s plus the phase of s convolved three times with itself with intermittent complex conjugation, weighted with w( However, an interesting scheme is to use an iterative procedure where the transmit beam is corrected with each new phase estimate of θ In the above calculations, we have used the Fourier transform of the received signal as a basis for the correlation analysis. The estimation then produces the phase amplitude screen over the complete range of frequencies in the received signal, i.e. both the 1st and the 2 Since the received signal contains noise, we will in practice only be able to estimate the screen for frequencies where the received signal has adequate power above the noise level. Eqs.(25, 27) for estimation of the screen amplitude is then conveniently modified to limit the estimated amplitude for frequencies with low signal power as where SN is a signal to noise ratio parameter and the subscript W indicates that the limitation is an approximation to a Wiener-type filter. This formula has a problem that the errors in the estimates produces ringing of the filter impulse response, which propagates through Eq.(3) into the corrected signals. Less ringing is obtained with a Matched filter type of approximation denoted with the subscript M as The region in ω where |s| is substantially larger than the noise, then defines frequency bands where estimation of the phase of s can be attempted, and the correction filter amplitude is set softly to zero at the edges of the bands. One should note that through inverse Fourier transform, the calculations can be done directly on the time varying received element signals according to well known transformations. In this respect, we note from Eq.(14) that the received, steering and focusing compensated signal can be written as where f(
_{f};ω)=a _{s}( r,r _{f})e ^{−iωτ} ^{ s } ^{(r,r } ^{ f } ^{)} (78)The inverse Fourier transform of s is then
_{f} ;t)=a _{s}( r, r _{f})δ{t−τ _{s}( r,r _{f}) (79)We note that the impulse response of the compensation filter in Eq.(3) is with this approximation
_{f} ;t)=F ^{−1} {H _{tr}( r,r _{f};ω)}=a _{s}( r,r _{f})δ{t+τ _{s}( r,r _{f}) (80)From Eq.(77) we see that we get the following form of the received signal in the temporal domain
a _{s}( r,r _{f})f( r,r _{f} ;t−τ _{s}( r,r _{f})) (81)The correlation function of the time signal y y _{f}( )r;ty _{f}( )>=r+ξ;t+τa _{s}( r,r _{f})a _{s}
_{f})R _{f}( r,ξ;τ+τ_{s}( r,r _{f})−τ_{s}( r+ξ,r _{f}))
f( r,r _{f} ;t)f( r+ξ,r _{f} ;t+τ)> (82)The amplitude can then be estimated from a frequency independent form of Eq.(22) as Using the result in Eq.(26) for Gaussian variables, we can use the modified expression To determine the delay correction τ
a _{s}( r,r _{f})f _{h}( r,r _{f} ;t−τ _{s}( r,r _{f})) (85)where f y _{f}( )r;ty _{fh}( )>=r+ξ;t+τ
_{f})a _{s}( r+ξ,r _{f})R _{fh}( r,ξ;τ+τ_{s}( r,r _{f})−τ_{s}( r+ξ,r _{f})
f( r,r _{f} ;t)f _{h}( r+ξ,rhd f;t+τ)> (86)For small
_{f})−τ_{s}( r,r _{f})=τ_{0} (87)The delays can hence be estimated based on the time functions of the element signals through correlation methods that are well developed. The delay approximations in Eqs.(78-82) are often found only in a limited band of frequencies, which requires that the received element signals are bandpass filtered to exclude noise, and other harmonic bands in the received signal. Especially if one wants to analyze a harmonic band of the received signal, one must bandpass filter the signals for this band to exclude the other harmonic components and noise. We note that this bears resemblance to the Fourier component analysis above, where the Fourier transform actually is a set of bandpass filters for each Fourier frequency component. By adequate band limiting the received element signals around a center frequency f where In a correlation process, it is sufficient to filter only one of the signals, as the filter also applies to the other signal in the correlation process. This is specially interesting for correlation with a reference signal as in Eqs.(68-74), as one then can band-pass filter and possibly Hilbert transform only the reference signal, as opposed to also filtering the much larger number of element signals. More specifically we get the reference signal of Eq.(68) in the temporal domain as where we for simplicity have neglected possible ω dependence of w in Eq.(68). Such ω variation of w could be included in this analysis also by an added convolution in time of the above expression. With the insertion of Eq.(79) we get with pure amplitude-delay screen Hilbert transforming and band-pass filtering this signal, for example to select a harmonic band, allows one to calculate the following correlation function where the subscripts mrh and mfh indicate bandpass filtering around the mth harmonic band and Hilbert transform, i.e.
_{a} , r−r _{a};τ)=<f( r _{a} , r _{f} ;t)f _{mh}( r,r _{f} ;t+τ)> (93)where the subscript mh indicates bandpass filtering around the mth harmonic band and Hilbert transform. In many practical situations one find that _{0})=0 τ_{0}≈τ_{s}( r,r _{f}) (94)This is specially true with iterated estimation schemes where the subgroup weighting function is extended to a filter w( The method of reference signal correlation hence leaves itself for simple processing both for harmonic filtering of any order, Hilbert transforms, etc., as this filtering can be done on the reference signal only, and not necessarily on all the element signals. This could also be formulated that the element signals contains unfiltered components that are uncorrelated to the filtered signals, these components hence being attenuated in the correlation process. Hence, reducing the sensitivity to stationary reverberations could be done only on the reference signal by harmonic band pass filtering or high pass filtering along the transmitted pulse number coordinate. However, in a practical correlation processes with averaging over limited number of samples, one will have rests of these signal components as variance in the final estimate depending on the total number of samples available for averaging. The variance can hence be reduced by filtering both signals before the correlation process. We also note that the formation of the reference signal produces a spatial lowpass filtering of the element signals along the array element coordinate, which reduces the effect of strong off-axis scatterers according to Eq.(59). To reduce the estimation variance in the averaging, it is still convenient to use additional averaging over the received signals from moving or time varying scatterers for many consecutive transmit pulses, so spaced apart in time that the scatterers are exchanged for each transmit pulse. The estimation of the amplitude corrections are based on simple expressions as in Eqs.(22, 25, 27, 75, 83, 84). The largest amount of processing goes into estimation of the phase of s, or the approximate delays of s, and these estimates are also subject to the largest estimation error. The spatial correlation length of the phase of s across the transducer surface, has in most situations a lower limit, which can be used to improve the variance and robustness of the estimates of both a For the screen phase θ where the coordinate on the receiver array is given as By renumbering the base functions, we can write Eq.(95) as where D One can then for example use the maximum likelihood method as in Eqs.(60-67) to estimate the coefficient vector Inserting this form of θ which is maximized when which is a non-linear equation in θ With an approximation of the screen as in Eq.(79), it is then natural to approximate the delay function as in Eq.(96), i.e. where D A block diagram of a possible implementation of the invention for distributed scatterers with short correlation length in an ultrasound imaging system, could be the same as shown in FIG. 3 Thus, while there have shown and described and pointed out fundamental novel features of the invention as applied to a preferred embodiment thereof, it will be understood that various omissions and substitutions and changes in the form and details of the devices illustrated, and in their operation, may be made by those skilled in the art without departing from the spirit of the invention. For example, it is expressly intended that all combinations of those elements and/or method steps which perform substantially the same function in substantially the same way to achieve the same results are within the scope of the invention. Moreover, it should be recognized that structures and/or elements and/or method steps shown and/or described in connection with any disclosed form or embodiment of the invention may be incorporated in any other disclosed or described or suggested form or embodiment as a general matter of design choice. It is the intention, therefore, to be limited only as indicated by the scope of the claims appended hereto. Patent Citations
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